Towards a kinetic theory of strings

Abstract

We study the dynamics of strings by means of a distribution function f(A, B, x, t) defined on a 9+1D phase space, where A and B are the correlation vectors of right- and left-moving waves. We derive a transport equation (an analogous to Boltzmann transport equation for particles) that governs the evolution of long strings with Nambu-Goto dynamics as well as reconnections taken into account. We also derive a system of coupled transport equations (an analogous to BBGKY hierarchy for particles) which can simultaneously describe long strings \tilde{f}(A, B, x, t) as well as simple loops \mathring{f}(A, B, x, t) made out of four correlation vectors. The formalism can be used to study non-linear dynamics of fundamental strings, D-brane strings or field theory strings. For example, the complicated semi-scaling behavior of cosmic strings translates into a simple solution of the transport system at small energy densities.

11 pages, 5 figures, improved transverse collisions, accepted for publication in Physical Review D

References in corpus (14)

• Cosmological evolution of cosmic string loops
• Large parallel cosmic string simulations: New results on loop production
• Fractal Properties and Small-scale Structure of Cosmic String Networks
• Scaling of cosmic string loops
• Cosmic string loops in the expanding universe
• Scaling and Small Scale Structure in Cosmic String Networks
• Analytic Study of Small Scale Structure on Cosmic Strings
• Cosmic String Loops, Large and Small
• Hot String Soup
• Cosmic string scaling in flat space
• Cosmic string loops: large and small, but not tiny
• Strings and D-Branes at High Temperature
• Semi-scaling cosmic strings
• Non-linear dynamics of cosmic strings with non-scaling loops

Cited by in corpus (10)

• Radio Broadcasts from Superconducting Strings
• CMB Distortions from Superconducting Cosmic Strings
• Cosmic string loop production functions
• Cosmic Strings as Emitters of Extremely High Energy Neutrinos
• Constraints on Superconducting Cosmic Strings from Early Reionization
• A Boltzmann treatment for the vorton excess problem
• Kinetic Theory and Hydrodynamics of Cosmic Strings
• Transport Equation for Nambu-Goto Strings
• Fluid Mechanics of Strings
• String Fluid in Local Equilibrium